76,158 research outputs found
Proof Generation from Delta-Decisions
We show how to generate and validate logical proofs of unsatisfiability from
delta-complete decision procedures that rely on error-prone numerical
algorithms. Solving this problem is important for ensuring correctness of the
decision procedures. At the same time, it is a new approach for automated
theorem proving over real numbers. We design a first-order calculus, and
transform the computational steps of constraint solving into logic proofs,
which are then validated using proof-checking algorithms. As an application, we
demonstrate how proofs generated from our solver can establish many nonlinear
lemmas in the the formal proof of the Kepler Conjecture.Comment: Appeared in SYNASC'1
Formal Verification of Molecular Computational Models in ACL2: A Case Study
Theorem proving is a classical AI problem with a broad range
of applications. Since its complexity is exponential in the size of the
problem, many methods to parallelize the process has been proposed.
One of these approaches is based on the massive parallelism of molecular
reactions. ACL2 is an automated theorem prover especially adequate for
algorithm verification. In this paper we present an ACL2 formalization
of a molecular computational model: Adleman’s restricted model. As
an application of this model, an implementation of Lipton’s experiment
solving SAT is described. We use ACL2 to make a formal proof of the
completeness and soundness properties of this implementation.Ministerio de Ciencia y Tecnología TIC2000-1368-C03-0
Validating specifications of dynamic systems using automated reasoning techniques
In this paper, we propose a new approach to validating formal specifications of observable behavior of discrete dynamic systems. By observable behavior we mean system behavior as observed by users or other systems in the environment of the system. Validation of a formal specification of an informal domain tries to answer the question whether the specification actually describes the intended domain. This differs from the verification problem, which deals with the correspondence between formal objects, e.g. between a formal specification of a system and an implementation of it. We consider formal specifications of object-oriented dynamic systems that are subject to static and dynamic integrity constraints. To validate that such a specification expresses the intended behavior, we propose to use a tool that can answer reachability queries. In a reachability query we ask whether the system can evolve from one state into another without violating the integrity constraints. If the query is answered positively, the system should exhibit an example path between the states; if the answer is negative, the system should explain why this is so. An example path produced by the tool can be used to produce scenarios for presentations of system behavior, but can also be used as a basis for acceptance testing. In this paper, we discuss the use of planning and theoremproving techniques to answer such queries, and illustrate the use of reachability queries in the context of information system development
Searching for a Solution to Program Verification=Equation Solving in CCS
International audienceUnder non-exponential discounting, we develop a dynamic theory for stopping problems in continuous time. Our framework covers discount functions that induce decreasing impatience. Due to the inherent time inconsistency, we look for equilibrium stopping policies, formulated as fixed points of an operator. Under appropriate conditions, fixed-point iterations converge to equilibrium stopping policies. This iterative approach corresponds to the hierarchy of strategic reasoning in game theory and provides “agent-specific” results: it assigns one specific equilibrium stopping policy to each agent according to her initial behavior. In particular, it leads to a precise mathematical connection between the naive behavior and the sophisticated one. Our theory is illustrated in a real options model
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LT revisited : explanation-based learning and the logic of Principia mathematica
This paper describes an explanation-based learning (EBL) system based on a version of Newell, Shaw and Simon's LOGIC-THEORIST (LT). Results of applying this system to propositional calculus problems from Principia Mathematica are compared with results of applying several other versions of the same performance element to these problems. The primary goal of this study is to characterize and analyze differences between not learning, rote learning (LT's original learning method), and EBL. Another aim is to provide base-line characterizations of the performance of a simple problem solver in the context of the Principa problems, in the hope that these problems can be used as a benchmark for testing improved learning methods, just as problems like chess and the eight puzzle have been used as benchmarks in research on search methods
Towards an Intelligent Tutor for Mathematical Proofs
Computer-supported learning is an increasingly important form of study since
it allows for independent learning and individualized instruction. In this
paper, we discuss a novel approach to developing an intelligent tutoring system
for teaching textbook-style mathematical proofs. We characterize the
particularities of the domain and discuss common ITS design models. Our
approach is motivated by phenomena found in a corpus of tutorial dialogs that
were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor
for textbook-style mathematical proofs can be built on top of an adapted
assertion-level proof assistant by reusing representations and proof search
strategies originally developed for automated and interactive theorem proving.
The resulting prototype was successfully evaluated on a corpus of tutorial
dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453
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